Arsène Wenger felt a mixture of pride and regret after his Arsenal team came within a fingertip of a historic Champions League comeback on Tuesday night. Having lost the first leg 4-0 in Milan, Arsenal's chances were written off. No side had ever overturned a four-goal deficit in Europe's elite competition. But three first-half goals put the home team on the brink of greatness, only for Milan to hold on for an aggregate win.

"We are disappointed because we touched qualification," Wenger said. "We had the chances. We didn't do it but we were very close. The players put in a faultless performance, with fantastic spirit, and you can only congratulate the whole team. It is a night when the players can be proud to play for this club. They put absolutely every effort in."

Having soared into a 3-0 lead, the search for the crucial fourth goal proved fruitless and Milan were indebted to their goalkeeper, Christian Abbiati, whose fingertip save from Robin van Persie in the second half proved decisive.

"What can I say?" Wenger mused. "The one you would want the chance to go to is Van Persie. But he wanted to chip the goalkeeper. You have to give credit to Abbiati; he came up very quickly."

Fatigue caught up with Arsenal, as well as a lack of options on the bench. Part of that is self-inflicted considering the attacking substitutes – Marouane Chamakh and Park Chu-young – are not seemingly made for the grandstand finish, though Wenger's frustration was that he could not bolster his midfield.

"I felt we suffered a bit in the second half physically because we had given a lot at Liverpool," he said. "Overall I felt we did not have many opportunities on the bench in midfield. In the second half we had more problems to keep the ball than the first half. The regret I have is there. We missed a player like [Mikel] Arteta, who had concussion."

The midfield impetus fell to Tomas Rosicky and Alex Oxlade-Chamberlain, both of whom drew praise from Arsenal's manager. He described Rosicky's contribution as "outstanding" and praised the Czech's influential contribution to the recent recovery that has seen Arsenal beat Tottenham, Liverpool and Milan in quick succession, scoring 10 goals in the process.

A generally positive night had a sour ending as Wenger became embroiled in an altercation with the referee, the Slovenian Damir Skomina, in the tunnel. Wenger was upset with a performance in which he believed the official gave too many fouls in Milan's favour. Arsenal conceded 21 fouls to Milan's eight. "I was not happy with the referee because he gave them many free-kicks in the centre of the park.

"Every single free-kick every time they went down it was for them. They sensed that very quickly on the pitch the players and they used it very well," he said. Skomina may include details of their exchange of views in his referee's report, which could land Wenger in some familiar hot water with Uefa.

It had echoes of the row with officialdom as Arsenal were knocked out of the Champions League last season at Barcelona. On that occasion Wenger was furious that Van Persie had been sent off by the Swiss referee Massimo Busacca, who gave the Arsenal striker a second booking for shooting when play had stopped even though Van Persie claimed he had not heard the whistle. Wenger received a touchline ban for that episode.

His bad feeling about the tie extended to another complaint about the pitch at San Siro, so if Uefa feels inclined to reprimand Wenger he would be inclined to say the feeling is mutual: "It's maybe an easy excuse but I feel Uefa has a lot to answer for because when you arrive at 7.46 you get fined but you can play on a bad pitch and they don't say a word. I just feel it is part of the respect for people who pay their money and go to a football game to at least put the game in conditions where people can play football. That's what we try to do here. It's unacceptable from Uefa that they accept pitches like we had in Milan."

At the end of it all, Arsenal's players looked shattered – physically and emotionally – and Wenger conceded it will be a tough job to pick them back up. "It will be difficult because it is a big disappointment for the players. The team has grown together and hopefully we can finish the season in a strong way because there is no room for disappointment in the league. For us every point is a battle; that is what is in front of us."

The lesson in this heroic but tragic saga is that you cannot lose 4-0 in the Champions League knockout rounds. Arsenal failed to show up in the San Siro and have paid the price in Europe, but I worry that there will be a spillover effect in the Premier League as well. It will be hard for the players to recover from last night's legendary but fruitless effort: the Ox picked up an injury, Rosicky is low on gas, Song must be exhausted. How will they muster the energy they need to finish fourth, or overtake Spurs?